1. 2E1242 Project Course Automatic Control - The Helicopter

2. The team David Höök Henric Jöngren Pontus Olsson Ksenija Orlovskaya Vivek Sharma

3. Resources Helicopter with two degrees of freedom (Humusoft) Input voltage to two DC motors driving the main and tail propellers (MIMO-system) Output horisontal and vertical angles Labview (communicating with process) Matlab (simulation, model validation)

4. The challenge MIMO system under influence of cross-coupling Modelling Many non directly measurable parameters Subsystems interlinked through many parameters

5. Main objective The helicopter is supposed to: Follow a prespecified trajectory that illustrates its performance limitations Attenuate external disturbances Hair-drier simulating hard wind Change of mass centre - adding a load to helicopter

6. Modelling Helicopter divided into subsystems Main motor and vertical movement Tail motor and horisontal movement Cross coupling: Main motor to horisontal movement (reaction torque) Horisontal movement to vertical movement (gyroscopic moment) Cross coupling from tail motor reaction to vertical moment and vertical gyro effects neglected.

7. Modelling Main motor and vertical movement

8. Modelling Tail motor and horisontal movement

9. Modelling Physically derived differential equation model

10. Modelling Black box First approach subsystem and model are compared

11. Modelling White box / Grey box Measure parameters corresponding to the physical model. Weight, distances Determine non directly measurable parameters Frictions, inertias, gyro, reaction torque – iteratively by adjusting parameters from model to fit responses from process ’ Time constants for motor dynamics Adjusting curves to static measurement data Functions mapping insignals to pull force, rotor velocity and reaction torque

12. Simulink model, vertical

13. Simulink model, horisontal

14. Simulink model, reaction torque

15. Simulink model, gyroscopic moment

16. Validation, vertical movement Step response of verticalmovement in model and process t

17. Validation, horisontal movement Step response of horisontal movement in model and process t

18. Validation, reaction torque Response in horisontal movement from step in main motor t t

19. Validation, gyroscopic effect Response in vertical movement from step in tail motor t

20. Validation, total model System too unstable to be validated open-loop Two manually tuned PID-controllers are used Model Process

21. Modelling Conclusion – what have we learned about modelling? More difficult than expected Dependent system Tuning a parameter of one subsystem will affect the behavior of other subsystems. Must find good balance between the best approximation of the separate subsystems and the performance of the total system. When is the model good enough? – When it is fulfilling its purpose White box: more insight and understanding of system than Black box Black box: less time consuming than white box

22. Control Different controllers Manually adjusted PID – one for each degree of freedom LQ controller with observer – one for the total system Is it necessary to spend weeks modelling if a quickly tuned P.I.D. can solve the control problem? -The manually adjusted PID against the model dependent LQ…

23. Control PID_vert G_vert u_vert(t) e_vert(t) r_vert(t) y_vert(t) + - PID_hor G_hor u_horizontal(t) e_hor(t) r_hor(t) y_hor(t) + - K2 Introducing cross gain – elimination of cross coupling Conclusion… Cross gain sK1 +

24. Validation, vertical movement Step response of verticalmovement in model and process t

25. Control LQ with observer - Not all states measureable - introducing state observer Observer Helicopter+ -L Fr r(t)u(t) y(t)

26. Control White noise with intensities: : Design variables : No covariance between the noise Model linearized by hand Equilibrium point taken from real process (input voltages and angles)

27. Control Singular values

28. Control LQPID

29. Control PID Easy and fast to derive and implement Possible to tune without modelling in some cases Compansates for static error caused by hair-drier Able to attenuate static error caused due to change in mass point Do not reduce cross coupling satisfactory LQ with observer Model dependent Better performace for a MIMO system with cross coupling Less oscillations Almost no overshoot Couldn’t attentuate static error caused due to change in mass point very well Many parameter need to be estimated. More complicated to derive and implement

30. Control Conclusion – what have we learned about control? - Different regulators: PID, LQ,close look at advantages and disadvantages over each other. - The functions are fulfilling their purposes.

31. THE END… 11/5 kl. 03.12